[ΔDM]ij= 
 |
[DM]ij |  if i ≠ j |
2 |
The entries in the detour-delta matrix, denoted by ΔDM, are related to the elements of the corresponding detour-path matrix as the entries of the vertex-distance-delta matrix are to the elements of vertex-distance matrix.
[ΔDM]ij= |
|
||||
| 0 otherwise (68) |
The detour-delta matrix enumerates the number of all the longest paths larger than unity between vertices i and j in a graph.
The ΔDM matrix of G1 (see structure A in Figure 2) is given below.
ΔDM(G1)= |
 |
0 |
0 |
1 |
10 |
6 |
10 |
15 |
 |
0 |
0 |
0 |
6 |
3 |
6 |
10 |
|||
1 |
0 |
0 |
3 |
1 |
3 |
6 |
|||
10 |
6 |
3 |
0 |
3 |
2 |
3 |
|||
6 |
3 |
1 |
3 |
0 |
3 |
6 |
|||
10 |
6 |
3 |
2 |
3 |
0 |
0 |
|||
15 |
10 |
6 |
3 |
6 |
0 |
0 |
The following relationship is between the elements of the three matrices based on the longest graph-distances DM, pDM and ΔDM:
[pDM]ij=[DM]ij + [ΔDM]ij (69)
